(/ 2.0 (* x (* (- (* x x)) 1.0)))

Average Error: 0.4 → 0.4

Time: 921.0ms

Precision: binary64

Math

\[\frac{2}{x \cdot \left(\left(-x \cdot x\right) \cdot 1\right)}\]

↓

\[\frac{\frac{2}{{x}^{3}}}{-1}\]

Error

Bits error versus x

Derivation

1. Initial program 0.4

   \[\frac{2}{x \cdot \left(\left(-x \cdot x\right) \cdot 1\right)}\]

2. Simplified 0.4

   \[\leadsto \color{blue}{\frac{\frac{2}{{x}^{3}}}{-1}}\]

3. Final simplification 0.4

   \[\leadsto \frac{\frac{2}{{x}^{3}}}{-1}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ 2.0 (* x (* (- (* x x)) 1.0)))"
  :precision binary64
  (/ 2.0 (* x (* (neg (* x x)) 1.0))))